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WO1997035264A1 - Procede et systeme de selection de vecteurs d'apprentissage a la reconnaissance de formes - Google Patents

Procede et systeme de selection de vecteurs d'apprentissage a la reconnaissance de formes Download PDF

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Publication number
WO1997035264A1
WO1997035264A1 PCT/US1997/003942 US9703942W WO9735264A1 WO 1997035264 A1 WO1997035264 A1 WO 1997035264A1 US 9703942 W US9703942 W US 9703942W WO 9735264 A1 WO9735264 A1 WO 9735264A1
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WO
WIPO (PCT)
Prior art keywords
clusters
example signals
cluster
pattern recognition
signals
Prior art date
Application number
PCT/US1997/003942
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English (en)
Inventor
James H. Errico
Theodore Mazurkiewicz
Original Assignee
Motorola, Inc.
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Motorola, Inc. filed Critical Motorola, Inc.
Priority to AU22093/97A priority Critical patent/AU2209397A/en
Publication of WO1997035264A1 publication Critical patent/WO1997035264A1/fr

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Classifications

    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/23—Clustering techniques
    • G06F18/232—Non-hierarchical techniques
    • G06F18/2321—Non-hierarchical techniques using statistics or function optimisation, e.g. modelling of probability density functions
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/24—Classification techniques
    • G06F18/245—Classification techniques relating to the decision surface
    • G06F18/2453—Classification techniques relating to the decision surface non-linear, e.g. polynomial classifier

Definitions

  • the present invention is related to the following inventions which are assigned to the same assignee as the present invention:
  • the present invention relates generally to pattern recognition systems and, in particular, to a method and system for deriving a set of training vectors usable with a pattern recognition system.
  • Pattern recognition systems are useful in a wide variety of technological areas such as image classification, target recognition and track, sonar, radar surveillance, medical diagnosis, speech and handwriting recognition.
  • a pattern recognition system is a device used to classify measurements (also know as features) that represent a set of patterns.
  • the structure of a recognition system typically includes a sensor for gathering pattern data, a feature extraction mechanism, and a classification algorithm.
  • pattern recognition systems see "Pattern Recognition Statistical, Structural, and Neural Approaches, R. Schalkoff, Wiley & Sons, 1992,
  • the feature extraction mechanism applies an extraction algorithm to the pattern data to produce a set of features.
  • features are any extractable measurement used by the system.
  • Features can be symbolic, numerical, or both.
  • An example of a symbolic feature is color; examples of numerical features are duration and velocity.
  • features can be arranged into an n-dimensional feature vector X, where ⁇ l f X2 / • • • • i ⁇ n are elements of X, each representing a different feature. This arrangement results in a multidimensional feature space. When n > 2, this space is commonly referred to as a hyperspace. If each feature is an unconstrained real number, the feature space is represented by R n . Typically, however, the feature space is restricted to a subspace of R n .
  • Feature extraction results in a representation of the pattern data that characterizes the relevant attributes thereof. It can be regarded as a data reduction procedure that retains vital characteristics of the pattern data while eliminating the undesirable interference from irrelevant characteristics. In turn, this eases the decision-making process of the classification algorithm.
  • Classification assigns pattern data into one or more prespecified classes based on the extracted features.
  • a class is a set of patterns having certain traits or attributes in common. For example, handwriting samples of the letter E could belong to the same class.
  • the task of a classification algorithm is to partition the feature space associated with the recognition system into separate regions for each class .
  • the border of each class region is known as a decision boundary. When n > 3, the boundary is a hyperplane.
  • a discriminant function is a mathematical equation that is used to define boundaries between class regions. Conventional discriminant functions include linear, quadratic, and Gaussian-based discriminant functions. The accurate determination of class regions has always been a challenge in the field of pattern recognition.
  • a fundamental problem to be solved by the classification algorithm is to accurately discern boundaries for class regions.
  • a classification algorithm or classifier (a device that implements the algorithm) establishes these boundaries based on known information, i.e., training sets.
  • Pattern recognition systems have two modes of operations: a training mode and a recognition mode.
  • Training uses representative examples of the types of pattern to be encountered in the actual application of the system.
  • the term supervised learning refers to a training mode in which the examples include respective class-labels. Basically, if enough example patterns within the classes to be recognized are provided, the training mode should be able to adequately characterized the properties of the classes so that unknown patterns can be reliably and repeatably classified across all such classes during the recognition mode.
  • prior art training techniques do not produce reliable classifiers for many types of patterns. Furthermore, these techniques are generally repetitive and require lengthy training sessions. For instance, recognition systems using neural networks as classifiers typically employ training techniques based on back propagation. Back propagation techniques require lengthy, repetitive training sessions that often yield unreliable classifiers.
  • FIG. 1 shows a flow diagram representing a method of selecting training vectors in accordance with a first embodiment of the present invention.
  • FIG. 2 shows a flow diagram representing a method of generating a polynomial discriminant function in accordance with a second embodiment of the present invention.
  • FIG. 3 shows a flow diagram representing a method of clustering example signals that can be used in the methods of FIGS. 1-2.
  • FIG. 4 is a graphical representation of an example space having an overlapping cluster.
  • FIG. 5 illustrates an exemplary result of applying an embodiment of the present invention to the example space of FIG. 4.
  • FIG. 6 shows a block diagram of a system for selecting training vectors in accordance with a third embodiment of the present invention.
  • FIG. 7 illustrates a system that can incorporate an embodiment of the present invention.
  • FIG. 8 is a detailed block diagram of the computer shown in FIG. 7.
  • FIG. 1 shows a flow diagram representing a method of selecting training vectors in accordance with one embodiment of the present invention.
  • a digital computer can be programmed to implement the method.
  • the training vectors, as well as all other signals mentioned herein, can be any form of electrical or optical signal.
  • a plurality of example signals is received. These signals are preferably digital words representing feature vectors from different classes within an example space. Additionally, each example signal includes a class label.
  • the example space is a feature space associated with the pattern recognition system for which the training vectors are being selected.
  • a plurality of clusters is defined.
  • Each cluster includes a class label and an identifier that indicates the location of the cluster within the example space.
  • the location identifier represents the cluster centroid.
  • Clusters are defined such that each cluster corresponds to patterns from the same class that are highly similar under a specific pattern dissimilarity measure. The measure can be based on spectral or Euclidean distances between example signals. Using distance, the clusters can be established by limiting each of the clusters to an intra-cluster distance that is less than a prespecified distance threshold.
  • the example signals are assigned to the clusters as a function of cluster-example distances.
  • each example signal is assigned to a closest cluster centroid by performing a nearest-neighbor search between the cluster centroids and the example signals. This results in a plurality of clusters that are populated with example signals. Some of these clusters may include example signals from different classes. An example signal having a class label that differs from that of its assigned cluster is referred to as an overlapping example signal.
  • decision box 26 a check is made to determine whether at least one of the class decision boundaries needs greater definition. If greater definition is needed, the number of clusters is increased (box 28) by defining new clusters. The procedure then returns to the step shown in box 24 to re-assigns the example signals to the augmented set of clusters.
  • the method continues to box 30.
  • the example signals from each of the clusters are sampled to select the training vectors.
  • the sampling can select different quantities of signals from the clusters, it is preferable to perform a uniform sampling of the clusters.
  • a set of training vectors is formed that is biased to include more examples in areas where the decision boundaries between classes need greater definition. This significantly improves the reliability of pattern classifiers because their training will emphasize distinguishing between classes that are otherwise easily confused.
  • the plurality of example signals within each of the classes can be clustered using a K-means clustering algorithm to produce a plurality of cluster centroids.
  • the example signals can be clustered using a binary-split algorithm.
  • the method checks whether one of the clusters includes a quantity of overlapping example signals that exceeds an overlap threshold.
  • the threshold is an integer greater than zero. If the threshold is exceeded, the number of clusters is increased (box 28) and the procedure returns to box 24. Otherwise, the method continues to box 30.
  • Cluster size is the number of example signals in a populated cluster. If the size of a cluster and the quantity of overlapping signals it contains are above acceptable minimum values, the method continues to box 30. Otherwise, the example signals of the cluster are excluded from further iterations of the steps to increase the number of clusters and re-assign examples (boxes 24-28) .
  • the determination is based on a ratio of the intra-cluster and inter-cluster distances.
  • the inter-cluster distance is the distance between cluster centroids. The method iterates the steps of boxes 24-28 until the ratio drops to an acceptable level or a maximum number of iterations has been performed.
  • the method of FIG. 1 optionally includes a step (not shown) of determining whether the classes represented by the example signals are reasonably separable.
  • the method can optionally attempt to increase the separability of the classes before proceeding with steps 22-30.
  • the separability of the classes can be increase by altering or increasing the dimensionality of the feature space.
  • FIG. 2 shows a flow diagram representing a method of generating a polynomial discriminant function in accordance with a second embodiment of the present invention.
  • a polynomial discriminant function is preferable because it can be "trained” to model decision boundaries without lengthy, repetitive training sessions. The discriminant function is then incorporated in a recognition system classifier.
  • a polynomial discriminant function is fitted to the training vectors. Although many different techniques can be used to fit the discriminant function to the vectors, a least squares estimation technique is preferably used to compute polynomial coefficients. In essence, the calculation of coefficients is how the discriminant function is trained.
  • the polynomial discriminant function is fitted to the set of training vectors representing examples from an n-dimensional feature space. If the number of terms in the polynomial is equal to the number of examples, a matrix-inversion technique may be employed to solve for the value of each coefficient. If the number of terms is not equal to the number of examples, a least-squares estimation technique is employed to solve for the value of each coefficient. Suitable least-squares estimation techniques include, for example, least-squares, extended least-squares, pseudo-inverse algorithm, Kalman filter, maximum-likelihood algorithm, Bayesian estimation, and the like.
  • the discriminant function is based on a polynomial expansion represented by:
  • Equation 1 xj represents the features; y represents the discriminant function output signal; w_ represents a coefficient; g j i represents an exponent; and i, j, m and n are integers.
  • the discriminant function is a second order polynomial expansion of the form:
  • Equation 2 ao represents a zero-order coefficient, bi represents a first-order coefficient, and cij represents a second-order coefficient, i and xj represent elements of an n-dimensional feature vector, y represents the discriminant function output signal, and i, j, m and n are integers.
  • the discriminant function can be based on an orthogonal function, such as a sine, cosine, exponential/logarithmic, Fourier transformation, Legendre polynomial, non-linear basis function such as a Volterra function or a radial basis function, or the like, or a combination of polynomial expansions and orthogonal functions.
  • an orthogonal function such as a sine, cosine, exponential/logarithmic, Fourier transformation, Legendre polynomial, non-linear basis function such as a Volterra function or a radial basis function, or the like, or a combination of polynomial expansions and orthogonal functions.
  • FIG. 3 shows a flow diagram representing a method of clustering example signals that can be used in the methods of FIGS. 1-2.
  • This method generates centroids that can be used to identify the locations of clusters in the example space.
  • the method of FIG. 3 is based on the K-means clustering algorithm, also referred to as the generalized Lloyd algorithm. However, in contrast to the K-means algorithm, the method of FIG. 3 iteratively increments the number of cluster centroid until the intra-cluster distances fall below a predefined threshold.
  • the cluster centroids are initialized by arbitrarily choosing a set of example signals to be the centroids.
  • a nearest-neighbor search is performed to assign each of the example signals to a closest cluster.
  • the search is performed for each signal by comparing the various distances between each cluster centroid and the signal.
  • the cluster centroids are updated. This is accomplished by calculating a new centroid based on the example signals assigned to the cluster in box 42.
  • the intra-cluster distance is computed for each cluster.
  • the intra-cluster distance is preferably the average distance between centroid and the assigned example signals.
  • decision box 48 a check is made to determine whether the cluster distances are less than a predefined threshold. Either the average of the intra-cluster distances, the maximum intra-cluster distance, or the inter-cluster distance can be used in this comparison.
  • the inter-cluster distance can be based on the distance between cluster centroids.
  • the threshold can be fixed in value or vary between iterations of the method steps. If the threshold is not exceeded, the method terminates and the current centroids are used to define the locations of the clusters. Otherwise, the method proceeds to box 50.
  • the number of cluster centroids is increased by selecting one or more example signals to represent additional centroids .
  • the method returns to box 42.
  • the steps of boxes 42-50 can be repeated until the intra-cluster distances falls below the threshold or the number of iterations exceeds a predefined limit.
  • the method may include a step that compares the rate of convergence of the cluster distances to determine whether the method steps should be repeated.
  • FIG. 4 is a graphical representation of an exemplary example space that includes overlapping signals. A two dimensional example space is depicted for conceptual simplicity. Two pattern classes are shown: an x-class and o-class. Members of the classes are identified in the example space by their respective symbols.
  • the example space of FIG. 4 can be thought of as representing a feature space after a first iteration of the method steps of boxes 20-24.
  • Three clusters 60-63 and their respective centroids 64-66 have been defined.
  • a first decision boundary 74 is arbitrarily chosen to separate the clusters according to class.
  • the first cluster 60 represents a sub-region of the o-class feature space, while the second and third clusters 61-63 represent sub-regions in the x-class feature space.
  • the first cluster 60 includes overlapping example signals, that is, examples of x-class patterns. Thus, if a classifier implements the first decision boundary 67, it is likely to misclassify x-patterns as o-patterns .
  • FIG. 5 illustrates an exemplary result of iteratively applying the steps of boxes 24-28 to the example space of FIG. 4.
  • An additional cluster 72 and its centroid 73 are defined.
  • the additional cluster 72 includes the overlapping example signals.
  • a refined decision boundary 75 can then be chosen to separate the clusters according to class. In this case, the decision boundary 75 reliably separates the classes, which reduces the likelihood of pattern misclassification.
  • FIG. 6 shows a block diagram of a system for selecting training vectors in accordance with a third embodiment of the present invention.
  • the computer- implementable system includes an input interface 90, a cluster processor 92, a sorter 94, a comparator 96, a selector 98, and a regression means 100.
  • the system can be implemented as a special purpose logic circuit or a combination of special purpose circuits and a microprocessor executing a computer program.
  • the input interface 90 receives the example signals described in conjunction with box 20.
  • the input interface 90 can include a bus interface circuit or software routines for transferring data into the system.
  • the cluster processor 92 defines the plurality of clusters described for FIG. 1 based on the example signal it receives from the input interface 90.
  • the sorter 94 assigns the example signals to the clusters as a function of a plurality of cluster-example distances.
  • the sorter 94 re-assigns the example signals to clusters in response to the comparator increasing the number cf clusters.
  • the comparator 96 determines whether one of the clusters includes overlapping example signals exceeds an overlap threshold. If the threshold is exceeded, the comparator increases the number clusters associated with the overlapping example signals.
  • the selector 98 selects the training vectors by a uniform sampling of example signals from each clusters.
  • the regression means 100 fits a polynomial expansion to the training vectors using a least squares estimate.
  • FIG. 7 illustrates a system that can incorporate an embodiment of the present invention, such as any of those shown in FIGS. 1, 2, and 6.
  • the system includes a computer 110 and a pattern recognition system 112. Either of the methods shown in FIGS. 1-2 could be implemented as steps in a computer program that is executable by the computer 110. Upon executing such a computer program, the computer 110 would pass results produced by the respective method (either selected training vectors or polynomial coefficients) to the pattern recognition system 112.
  • the pattern recognition system 112 is detachably connected to the computer 110.
  • the pattern recognition system 112 In the event that the computer 110 produces training vectors, the pattern recognition system 112 would enter a training mode upon receiving these vectors. After completion of training with the vectors, the pattern recognition system could enter a recognition mode.
  • the computer 110 would allow the pattern recognition system 112 to directly enter the recognition mode without first executing the training mode. This could simplify the pattern recognition system 112.
  • FIG. 8 is a detailed block diagram of the computer 110 shown in FIG. 7.
  • the computer 110 is a general purpose computer that includes a central processing unit (CPU) 120, a memory 122, a processor bus 124, a peripheral interface 126, a peripheral bus 128, and a mass storage device 130.
  • CPU central processing unit
  • the CPU 120 executes programs that are stored in either the memory 122 or the mass storage device 130. Data is transferred between the CPU 120, memory 122, and peripheral interface 126 by way of processor bus 124.
  • the peripheral interface 126 includes circuitry for transferring data between the devices connected to the processor bus 124 and devices connected to the peripheral bus 128. Generally, the processor bus 124 operates at higher speeds than the peripheral bus 128.
  • the mass storage device 130 can be any device for storing computer-readable data, such as a disk drive, tape drive, or memory circuit.
  • a computer program that includes the method steps of FIGS. 1-2 can be stored in either the memory 122 or the mass storage device 130. Such a program can be executed by the CPU 120.
  • the system shown in FIG. 6 can be implemented in the computer 110 as any number of different combinations of software and hardware components.
  • elements 90-100 of the system could be implemented in an application specific integrated circuit (ASIC) or a special purpose circuit board having discrete logic circuits.
  • ASIC application specific integrated circuit
  • Such an ASIC or circuit board could be attached to either the processor bus 124 or the peripheral bus 128.
  • the pattern recognition system 112 is connected to the peripheral bus 128.
  • the recognition system 112 can be optionally connected to the processor bus 124.
  • the method steps of FIG. 1 or FIG. 2 and the pattern recognition system 112 are implemented as routines in a computer program that is storable in memory 122 or mass storage device 130 and executable by CPU 120.
  • the method and system of selecting training vectors or generating discriminant coefficients is implemented as an article of manufacture.
  • the article of manufacture includes a computer-readable memory usable for causing a computer to select training vectors for a pattern recognition system.
  • the article of manufacture is produced by the act of storing a computer program in the computer-readable memory, where the computer program includes either of the methods described in conjunction with FIGS. 1-2.
  • the computer-readable memory could be any means for storing a computer program, including the memory circuit 122, the mass storage device 130, or a CD-ROM, hard disk drive, floppy disk, ROM, or RAM.

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Abstract

La présente invention concerne un procédé et un système susceptibles de sélectionner des vecteurs d'apprentissage pour un système de reconnaissance des formes. On crée un ensemble de groupes (22) et on procède à l'échantillonnage desdits groupes. Chacun des groupes est apparenté à une classe particulière et comprend un ensemble de signaux d'exemple. Les signaux d'exemple sont affectés aux groupes en fonction des écarts (24) d'exemples par groupe. Si un groupe comporte un ou plusieurs signaux d'exemple semblables, le nombre de groupes apparentés au groupe ayant des signaux d'exemple semblables est incrémenté (28) et les signaux d'exemple sont réaffectés audits groupes.
PCT/US1997/003942 1996-03-19 1997-03-13 Procede et systeme de selection de vecteurs d'apprentissage a la reconnaissance de formes WO1997035264A1 (fr)

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US08/618,223 US5796924A (en) 1996-03-19 1996-03-19 Method and system for selecting pattern recognition training vectors
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FR2746530A1 (fr) 1997-09-26

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